Mathematics for Physicists and Engineers
Fundamentals and Interactive Study Guide
Seiten
2009
|
2010. Auflage
Springer Berlin
978-3-642-00172-7 (ISBN)
Springer Berlin
978-3-642-00172-7 (ISBN)
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Mathematics is the basic language in physics and engineering. This textbook offers an accessible and highly-effective approach to mathematics which is characterised by the combination of the textbook with a detailed study guide on an accompanying CD.
Mathematicsisanessentialtoolforphysicistsandengineerswhichstudentsmust usefromtheverybeginningoftheirstudies. Thiscombinationoftextbookandstudy guideaimstodevelopasrapidlyaspossiblethestudents’abilitytounderstandand tousethosepartsofmathematicswhichtheywillmostfrequentlyencounter. Thus functions,vectors,calculus,differentialequationsandfunctionsofseveralvariables arepresentedin averyaccessible way. Furtherchaptersinthe bookprovidethe basicknowledgeonvariousimportanttopicsinappliedmathematics. Basedontheirextensiveexperienceaslecturers,eachoftheauthorshasacquired acloseawarenessoftheneedsof rst-andsecond-yearsstudents. Oneoftheiraims hasbeentohelpuserstotacklesuccessfullythedif cultieswithmathematicswhich are commonlymet. A special feature which extendsthe supportivevalue of the maintextbookistheaccompanying“studyguide”. Thisstudyguideaimstosatisfy twoobjectivessimultaneously:itenablesstudentstomakemoreeffectiveuseofthe maintextbook,anditoffersadviceandtrainingontheimprovementoftechniques onthestudyoftextbooksgenerally. Thestudyguidedividesthewholelearningtaskintosmallunitswhichthes- dentisverylikelytomastersuccessfully. Thusheorsheisaskedtoreadandstudy alimitedsectionofthetextbookandtoreturntothestudyguideafterwards. Lea- ingresultsarecontrolled,monitoredanddeepenedbygradedquestions,exercises, repetitionsand nallybyproblemsandapplicationsofthecontentstudied. Sincethe degreeofdif cultiesisslowlyrisingthestudentsgaincon denceimmediatelyand experiencetheirownprogressinmathematicalcompetencethusfosteringmoti- tion. Incaseoflearningdif cultiesheorsheisgivenadditionalexplanationsandin caseofindividualneedssupplementaryexercisesandapplications. Sothesequence ofthestudiesisindividualisedaccordingtotheindividualperformanceandneeds andcanberegardedasafulltutorialcourse. TheworkwasoriginallypublishedinGermanyunderthetitle“Mathematikfür Physiker”(Mathematicsforphysicists). Ithasproveditsworthinyearsofactual use. Thisnew internationalversionhasbeenmodi edand extendedto meet the needsofstudentsinphysicsandengineering. vii viii Preface TheCDofferstwoversions. Ina rstversiontheframesofthestudyguideare presentedonaPCscreen. Inthiscasetheuserfollowstheinstructionsgivenonthe screen,at rststudyingsectionsofthetextbookoffthePC. Afterthisautonomous studyheistoanswerquestionsandtosolveproblemspresentedbythePC. Asecond versionisgivenaspdf lesforstudentspreferringtoworkwithaprintversion. Boththetextbookandthestudyguidehaveresultedfromteamwork. The- thors of the original textbook and study guides were Prof. Dr. Weltner, Prof. Dr. P. -B. Heinrich,Prof. Dr. H. Wiesner,P. EngelhardandProf. Dr. H. Schmidt. Thetranslationandtheadaptionwasundertakenbytheundersigned. Frankfurt,August2009 K. Weltner J. Grosjean P. Schuster W. J. Weber Acknowledgement OriginallypublishedintheFederalRepublicofGermanyunderthetitle MathematikfürPhysiker bytheauthors K. Weltner,H. Wiesner,P. -B. Heinrich,P. EngelhardtandH. Schmidt. TheworkhasbeentranslatedbyJ. GrosjeanandP. Schusterandadaptedtotheneeds ofengineeringandsciencestudentsinEnglishspeakingcountriesbyJ. Grosjean, P. Schuster,W. J. WeberandK. Weltner. ix Contents Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii 1 VectorAlgebraI:ScalarsandVectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 1 ScalarsandVectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 2 AdditionofVectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1. 2. 1 SumofTwoVectors:GeometricalAddition . . . . . . . . . . . . . 4 1. 3 SubtractionofVectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1. 4 ComponentsandProjectionofaVector . . . . . . . . . . . . . . . . . . . . . . . 7 1. 5 ComponentRepresentationinCoordinateSystems. . . . . . . . . . . . . . 9 1. 5. 1 PositionVector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1. 5. 2 UnitVectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1. 5. 3 ComponentRepresentationofaVector . . . . . . . . . . . . . . . . . 11 1. 5. 4 RepresentationoftheSumofTwoVectors inTermsofTheirComponents. . . . . . . . . . . . . . . . . . . . . . . . 12 1. 5. 5 SubtractionofVectorsinTermsoftheirComponents. . . . . 13 1. 6 MultiplicationofaVectorbyaScalar. . . . . . . . . . . . . . . . . . . . . . . . . 14 1. 7 MagnitudeofaVector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2 VectorAlgebraII:ScalarandVectorProducts. . . . . . . . . . . . . . . . . . . . 23 2. 1 ScalarProduct . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2. 1. 1 Application:EquationofaLineandaPlane. . . . . . . . . . . . . 26 2. 1. 2 SpecialCases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2. 1. 3 CommutativeandDistributiveLaws. . . . . . . . . . . . . . . . . . . . 27 2. 1. 4 ScalarProductinTermsoftheComponentsoftheVectors. 27 2. 2 VectorProduct. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2. 2. 1 Torque. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2. 2. 2 TorqueasaVector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2. 2. 3 De nitionoftheVectorProduct. . . . . . . . . . . . . . . . . . . . . . .
Mathematicsisanessentialtoolforphysicistsandengineerswhichstudentsmust usefromtheverybeginningoftheirstudies. Thiscombinationoftextbookandstudy guideaimstodevelopasrapidlyaspossiblethestudents’abilitytounderstandand tousethosepartsofmathematicswhichtheywillmostfrequentlyencounter. Thus functions,vectors,calculus,differentialequationsandfunctionsofseveralvariables arepresentedin averyaccessible way. Furtherchaptersinthe bookprovidethe basicknowledgeonvariousimportanttopicsinappliedmathematics. Basedontheirextensiveexperienceaslecturers,eachoftheauthorshasacquired acloseawarenessoftheneedsof rst-andsecond-yearsstudents. Oneoftheiraims hasbeentohelpuserstotacklesuccessfullythedif cultieswithmathematicswhich are commonlymet. A special feature which extendsthe supportivevalue of the maintextbookistheaccompanying“studyguide”. Thisstudyguideaimstosatisfy twoobjectivessimultaneously:itenablesstudentstomakemoreeffectiveuseofthe maintextbook,anditoffersadviceandtrainingontheimprovementoftechniques onthestudyoftextbooksgenerally. Thestudyguidedividesthewholelearningtaskintosmallunitswhichthes- dentisverylikelytomastersuccessfully. Thusheorsheisaskedtoreadandstudy alimitedsectionofthetextbookandtoreturntothestudyguideafterwards. Lea- ingresultsarecontrolled,monitoredanddeepenedbygradedquestions,exercises, repetitionsand nallybyproblemsandapplicationsofthecontentstudied. Sincethe degreeofdif cultiesisslowlyrisingthestudentsgaincon denceimmediatelyand experiencetheirownprogressinmathematicalcompetencethusfosteringmoti- tion. Incaseoflearningdif cultiesheorsheisgivenadditionalexplanationsandin caseofindividualneedssupplementaryexercisesandapplications. Sothesequence ofthestudiesisindividualisedaccordingtotheindividualperformanceandneeds andcanberegardedasafulltutorialcourse. TheworkwasoriginallypublishedinGermanyunderthetitle“Mathematikfür Physiker”(Mathematicsforphysicists). Ithasproveditsworthinyearsofactual use. Thisnew internationalversionhasbeenmodi edand extendedto meet the needsofstudentsinphysicsandengineering. vii viii Preface TheCDofferstwoversions. Ina rstversiontheframesofthestudyguideare presentedonaPCscreen. Inthiscasetheuserfollowstheinstructionsgivenonthe screen,at rststudyingsectionsofthetextbookoffthePC. Afterthisautonomous studyheistoanswerquestionsandtosolveproblemspresentedbythePC. Asecond versionisgivenaspdf lesforstudentspreferringtoworkwithaprintversion. Boththetextbookandthestudyguidehaveresultedfromteamwork. The- thors of the original textbook and study guides were Prof. Dr. Weltner, Prof. Dr. P. -B. Heinrich,Prof. Dr. H. Wiesner,P. EngelhardandProf. Dr. H. Schmidt. Thetranslationandtheadaptionwasundertakenbytheundersigned. Frankfurt,August2009 K. Weltner J. Grosjean P. Schuster W. J. Weber Acknowledgement OriginallypublishedintheFederalRepublicofGermanyunderthetitle MathematikfürPhysiker bytheauthors K. Weltner,H. Wiesner,P. -B. Heinrich,P. EngelhardtandH. Schmidt. TheworkhasbeentranslatedbyJ. GrosjeanandP. Schusterandadaptedtotheneeds ofengineeringandsciencestudentsinEnglishspeakingcountriesbyJ. Grosjean, P. Schuster,W. J. WeberandK. Weltner. ix Contents Preface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii 1 VectorAlgebraI:ScalarsandVectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 1 ScalarsandVectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1. 2 AdditionofVectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1. 2. 1 SumofTwoVectors:GeometricalAddition . . . . . . . . . . . . . 4 1. 3 SubtractionofVectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1. 4 ComponentsandProjectionofaVector . . . . . . . . . . . . . . . . . . . . . . . 7 1. 5 ComponentRepresentationinCoordinateSystems. . . . . . . . . . . . . . 9 1. 5. 1 PositionVector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1. 5. 2 UnitVectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1. 5. 3 ComponentRepresentationofaVector . . . . . . . . . . . . . . . . . 11 1. 5. 4 RepresentationoftheSumofTwoVectors inTermsofTheirComponents. . . . . . . . . . . . . . . . . . . . . . . . 12 1. 5. 5 SubtractionofVectorsinTermsoftheirComponents. . . . . 13 1. 6 MultiplicationofaVectorbyaScalar. . . . . . . . . . . . . . . . . . . . . . . . . 14 1. 7 MagnitudeofaVector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2 VectorAlgebraII:ScalarandVectorProducts. . . . . . . . . . . . . . . . . . . . 23 2. 1 ScalarProduct . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2. 1. 1 Application:EquationofaLineandaPlane. . . . . . . . . . . . . 26 2. 1. 2 SpecialCases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2. 1. 3 CommutativeandDistributiveLaws. . . . . . . . . . . . . . . . . . . . 27 2. 1. 4 ScalarProductinTermsoftheComponentsoftheVectors. 27 2. 2 VectorProduct. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2. 2. 1 Torque. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2. 2. 2 TorqueasaVector. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2. 2. 3 De nitionoftheVectorProduct. . . . . . . . . . . . . . . . . . . . . . .
Klaus Weltner ist an der Universität Frankfurt tätig.
Peter Schuster, geboren 1957, lehrte von 2006 bis 2010 als Professor an der Universität des Saarlandes. 2009 war er "Professeur inivité" an der "École des Hautes Études en Sciences Sociales" in Paris. Seit 2011 ist er Professor für die Geschichte des Mittelalters und der Frühen Neuzeit an der Universität Bielefeld.
Vector Algebra I: Scalars and Vectors.- Vector Algebra II: Scalar and Vector Products.- Functions.- Exponential, Logarithmic and Hyperbolic Functions.- Differential Calculus.- Integral Calculus.- Applications of Integration.- Taylor Series and Power Series.- Complex Numbers.- Differential Equations.- Laplace Transforms.- Functions of Several Variables; Partial Differentiation; and Total Differentiation.- Multiple Integrals; Coordinate Systems.- Transformation of Coordinates; Matrices.- Sets of Linear Equations; Determinants.- Eigenvalues and Eigenvectors of Real Matrices.- Numerical Methods.- Fourier Series; Harmonic Analysis.- Probability Calculus.- Probability Distributions.- Theory of Errors.
| Sprache | englisch |
|---|---|
| Maße | 155 x 235 mm |
| Gewicht | 988 g |
| Themenwelt | Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika |
| Schlagworte | Calculus • elearning physics • Hardcover, Softcover / Physik, Astronomie/Allgemeines, Lexika • learning • mathematics engineering • mathematics physics • Mathematik; Handbuch/Lehrbuch • Numerical Methods • Potential • textbook mathematical physics • textbook math engineering • textbook math physics • Transformation |
| ISBN-10 | 3-642-00172-6 / 3642001726 |
| ISBN-13 | 978-3-642-00172-7 / 9783642001727 |
| Zustand | Neuware |
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